The Exercise 5 needed is below

6 Let Ct be as in Exercise 5 and let Pt be the value of an American put option on the same stock with the same strike price and maturity. By comparing the values of two suitable portfolios, show that Ct + K > Pt + St. Using put-call parity for European options and the result of Exercise 5, show that Pt > Ct + Ke=r(T-t) St. Combine these results to see that, if r > 0 and t 0, prove that Ct > St Ke-r(T-1) > St K, and deduce that it is never optimal to exercise this option prior to the maturity time, T. 6 Let Ct be as in Exercise 5 and let Pt be the value of an American put option on the same stock with the same strike price and maturity. By comparing the values of two suitable portfolios, show that Ct + K > Pt + St. Using put-call parity for European options and the result of Exercise 5, show that Pt > Ct + Ke=r(T-t) St. Combine these results to see that, if r > 0 and t 0, prove that Ct > St Ke-r(T-1) > St K, and deduce that it is never optimal to exercise this option prior to the maturity time, T